Question

if an angle of a parallelogram is 2/3 of its adjacent angle the smallest angle of a parallelogram will be
54 degree, 72 degree ,108 degree​

Answer 1

Answer:

72°

Step-by-step explanation:

The sum of adjacent angle of parallelogram=180°

Let us take the adjacent angle as x

∴The original angle will be 2x/3

∴2x/3+x=180°

Equalizing the denominator,

2x+3x/3=180°

5x/3=180

5x=180×3

5x=540

x=540/5

x=108°

∴2x/3=108×2/3=72°

Since the opposite angles of a parallelogram are equal

The measures of the 4 angles are 72°,108°,72°,108°

∴The measure of smallest angle is 72°

Answer 2

Answer:

72°

Step-by-step explanation:

adj angles of parallelogram are supplementary

x + y = 180°

x = 2/3y

2/3y + y = 180°

5y/3 = 180°

y = 108°

x = 180° - 108° = 72°

smallest angle = x = 72°